A new algorithm for the small-field astrometric point-pattern matching problem

  • Cláudio P. Santiago
  • Carlile Lavor
  • Sérgio Assunção Monteiro
  • Alberto Kroner-Martins
Article
  • 6 Downloads

Abstract

The small-field astrometric point-pattern matching problem is a fundamental problem in astronomy, that although considered a long time ago still lacks a formal definition. It can be textually stated as: given two lists of positions of stars, find the common stars between these lists, taking into account rotation, translation, reflection and scaling operations. It is expected that there might be missing stars between the lists. In this work, we give the astronomical context, review some heuristic methods adopted in the literature, present distance matrix formulations for the problem and propose a new algorithm to solve it.

Keywords

Distance matrix Astronomy Astrometry Point-pattern matching 

Notes

Acknowledgements

This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. We also thank the support of the Brazilian Agencies CNPq, FAPESP, and FAPERJ. We would like to thank the anonymous reviewers for the helpful comments provided on earlier drafts of the manuscript.

References

  1. 1.
    Groombridge, S., Airy, G.B.: A Catalogue of Circumpolar Stars. BiblioBazaar, Charleston (2009)Google Scholar
  2. 2.
    Groth, E.J.: A pattern-matching algorithm for two-dimensional coordinate lists. Astron. J. 91(5), 1244–1248 (1986)CrossRefGoogle Scholar
  3. 3.
    Howard, A.W., Marcy, G.W., Fischer, D.A., Isaacson, H., Muirhead, P.S., Henry, G.W., Boyajian, T.S., Braun, K., Becker, J.C., Wright, J.T.: The NASA-UC-UH ETA-earth program. IV. A low-mass planet orbiting an M dwarf 3.6 PC from earth. Astrophys. J. 794(1), 51–59 (2014)CrossRefGoogle Scholar
  4. 4.
    Lang, D., Hogg, D.W., Mierle, K., Blanton, M., Roweis, S.: Astrometry.net: blind astrometric calibration of arbitrary astronomical images. Astron. J. 139, 1782–1800 (2010)CrossRefGoogle Scholar
  5. 5.
    Liberti, L., Lavor, C., Maculan, N., Mucherino, A.: Euclidean distance geometry and applications. SIAM Rev. 56(1), 3–69 (2014)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Meyer, C.D.: Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia (2000)CrossRefGoogle Scholar
  7. 7.
    Murtagh, F.: A new approach to point-pattern matching. Publ. Astron. Soc. Pac. 104, 301–307 (1992)CrossRefGoogle Scholar
  8. 8.
    Pal, A., Bakos, G.: Astrometry in wide-field surveys. Publ. Astron. Soc. Pac. 118(848), 1474–1483 (2006)CrossRefGoogle Scholar
  9. 9.
    Stetson, P.B.: The techniques of least squares and stellar photometry with CCDs. Vth IAG-USP Advanced School of Astrophysics (1989). http://nedwww.ipac.caltech.edu/level5/Stetson/Stetson5_2.html. Accessed Feb 2017
  10. 10.
    Tabur, V.: Fast algorithms for matching CCD images to a stellar catalogue. Publ. Astron. Soc. Austral. 24, 189–198 (2007)CrossRefGoogle Scholar
  11. 11.
    Valdes, F.G., Campusano, L.E., Velasquez, J.D., Stetson, P.B.: FOCAS automatic catalog matching algorithm. Publ. Astron. Soc. Pac. 107, 1119–1128 (1995)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Applied Scientific ComputingLawrence Livermore National LaboratoryLivermoreUSA
  2. 2.University of Campinas (IMECC - UNICAMP)CampinasBrazil
  3. 3.UFRJ - Federal University of Rio de JaneiroRio de JaneiroBrazil
  4. 4.SIM - Universidade de LisboaLisboaPortugal

Personalised recommendations